Arsenal supporters are regularly presented with betting odds as though they are a straightforward measure of what is likely to happen next.
A short price for an Arsenal win can make three points look almost inevitable, while changes in the title market are often treated as a running verdict on the team’s chances.
But bookmaker prices are not neutral predictions. They are commercial prices, and built into them is a margin which matters when trying to work out what the numbers actually mean.
The starting point is implied probability.
With decimal odds, that is calculated by dividing one by the price and multiplying by 100. Odds of 2.00 imply a probability of 50 per cent, 4.00 implies 25 per cent and 1.25 implies 80 per cent.
Decimal prices also include the returned stake. A successful £10 bet at 4.00 therefore returns £40 in total, made up of £30 profit and the original £10.
The more interesting part comes when you look at an entire football market rather than one team’s price in isolation.
Before Arsenal played Hull City on 7 November, The Telegraph listed prices of 1/6 for Arsenal to win, 13/2 for the draw and 16/1 for Hull. Those were the prices recorded in that article and not necessarily the final odds available before kick-off.
Converted into decimal form, Arsenal’s 1/6 becomes roughly 1.1667, which implies an 85.71 per cent chance of victory.
The draw at 13/2 becomes 7.50, implying 13.33 per cent, while Hull at 16/1 becomes 17.00, implying 5.88 per cent.
Add those three figures together and you get approximately 104.93 per cent.
Clearly, there is not a 104.93 per cent chance of something happening in a market where an Arsenal win, a draw and a Hull win cover every possible result.
That extra 4.93 percentage points is the overround, the surplus built into the bookmaker’s prices.
It is an indication of the margin contained across that particular market, rather than another possible outcome on the pitch.
It is also important not to turn that figure into something it is not.
A 4.93 per cent overround does not mean the bookmaker is guaranteed to make £4.93 for every £100 wagered. The actual financial result depends on where the money has been staked and what happens in the match.
The overround describes the pricing of the market, not the bookmaker’s eventual profit from it.
One way of stripping that surplus out is to divide each implied probability by the combined total. Doing so scales the three figures back to 100 per cent.
That can provide a cleaner view of the market, but it rests on the assumption that the margin has been applied proportionally across all three outcomes. It should not be treated as uncovering independently verified “true” probabilities.
A casino game offers a useful comparison because, with specified rules and payouts, the mathematical house edge can be calculated directly.
Standard European roulette has 37 pockets, including one zero. A winning bet on a single number pays 35/1, returning £36 including the original £1 stake.
With one winning number from 37 possible pockets, that produces a house edge of roughly 2.70 per cent.
That figure is fixed under those particular rules and payouts, even though the result for an individual player can vary wildly over a short period.
The situation becomes less straightforward when discussing gambling operators more generally.
Madison Casino, for example, is a licensed Belgian operator whose published terms identify its B+3320 licence and explain its return-to-player arrangements. Those terms also allow RTP adjustments, meaning it would be wrong to suggest every game on the site carries one permanent, universal house edge.
Its Belgian licensing should not be confused with authorisation in the UK, either.
That distinction matters because a bookmaker’s football margin and a casino game’s mathematical house edge are not the same thing.
In football betting, the margin is spread across prices and can vary from one market to another. In a game such as roulette, the edge can be calculated from fixed rules and payouts.
For Arsenal supporters, the useful lesson is simpler.
A betting price can tell you something about how a market is being assessed, but it is still a price offered by a business.
Looking at the full market, and the margin built into it, provides a much clearer picture than taking Arsenal’s quoted odds and treating them as a direct forecast of what is going to happen.